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  2. Derivative - Wikipedia

    en.wikipedia.org/wiki/Derivative

    In mathematics, the derivative is a fundamental tool that quantifies the sensitivity to change of a function's output with respect to its input. The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point.

  3. Arithmetic derivative - Wikipedia

    en.wikipedia.org/wiki/Arithmetic_derivative

    For example, the regular derivative is the arithmetic derivative for the rings of univariate real and complex polynomial and rational functions, which can be proven using the fundamental theorem of algebra. The arithmetic derivative has also been extended to the ring of integers modulo n. [7]

  4. Third derivative - Wikipedia

    en.wikipedia.org/wiki/Third_derivative

    In calculus, a branch of mathematics, the third derivative or third-order derivative is the rate at which the second derivative, or the rate of change of the rate of change, is changing. The third derivative of a function y = f ( x ) {\displaystyle y=f(x)} can be denoted by

  5. Differential of a function - Wikipedia

    en.wikipedia.org/wiki/Differential_of_a_function

    A number of properties of the differential follow in a straightforward manner from the corresponding properties of the derivative, partial derivative, and total derivative. These include: [ 11 ] Linearity : For constants a and b and differentiable functions f and g , d ( a f + b g ) = a d f + b d g . {\displaystyle d(af+bg)=a\,df+b\,dg.}

  6. Differentiation rules - Wikipedia

    en.wikipedia.org/wiki/Differentiation_rules

    These rules are given in many books, both on elementary and advanced calculus, in pure and applied mathematics. Those in this article (in addition to the above references) can be found in: Mathematical Handbook of Formulas and Tables (3rd edition), S. Lipschutz, M.R. Spiegel, J. Liu, Schaum's Outline Series, 2009, ISBN 978-0-07-154855-7.

  7. Differential calculus - Wikipedia

    en.wikipedia.org/wiki/Differential_calculus

    One way of improving the approximation is to take a quadratic approximation. That is to say, the linearization of a real-valued function f(x) at the point x 0 is a linear polynomial a + b(xx 0), and it may be possible to get a better approximation by considering a quadratic polynomial a + b(xx 0) + c(xx 0) 2.

  8. Derivation (differential algebra) - Wikipedia

    en.wikipedia.org/wiki/Derivation_(differential...

    In mathematics, a derivation is a function on an algebra that generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D : A → A that satisfies Leibniz's law: = + ().

  9. Differential (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Differential_(mathematics)

    For example, if x is a variable, then a change in the value of x is often denoted Δx (pronounced delta x). The differential dx represents an infinitely small change in the variable x. The idea of an infinitely small or infinitely slow change is, intuitively, extremely useful, and there are a number of ways to make the notion mathematically ...

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